Free quantum field theory in flat space-time is often believed to be well established, holding no surprises. We hope, by the end of this paper, to have demonstrated that surprises still exist. For example, we will show that a uniformly accelerated atom in Minkowski space-time emits entangled photon pairs in a squeezed state which mimics entanglement of the Minkowski vacuum in that the entanglement is between Minkowski modes which are dominantly in opposite causal wedges of the space-time. Similar emission of photon pairs occurs if an atom is held above the black hole event horizon. Namely, a ground-state atom becomes excited by emitting a ``negative'' -energy photon under the horizon and then spontaneously decays back to the ground state by emitting a positive-energy photon outside the horizon, which propagates away from the black hole.
Free quantum field theory in flat space-time is often believed to be well established, holding no surprises. We hope, by the end of this paper, to have demonstrated that surprises still exist. For example, we will show that a uniformly accelerated atom in Minkowski space-time emits entangled photon pairs in a squeezed state which mimics entanglement of the Minkowski vacuum in that the entanglement is between Minkowski modes which are dominantly in opposite causal wedges of the space-time. Similar emission of photon pairs occurs if an atom is held above the black hole event horizon. Namely, a ground-state atom becomes excited by emitting a ``negative'' -energy photon under the horizon and then spontaneously decays back to the ground state by emitting a positive-energy photon outside the horizon, which propagates away from the black hole.
Emission of photons by atoms can occur into modes which extend into a region causally disconnected with the emitter.For example, a uniformly accelerated ground-state atom emits a photon into the Unruh-Minkowski mode which is exponentially larger in the causally disconnected region.This makes an impression that photon emission is acausal.Here we show that conventional quantum optical analysis yields that a detector atom will not detect the emitted photon in the region noncausally connected with the emitter.However, joint excitation probability of atoms in the causally disconnected regions can be correlated due to entanglement of Minkowski vacuum and be much larger than the product of independent excitation probabilities.Moreover, atoms uniformly accelerated in the same Rindler wedge cannot become simultaneously excited without changing the state of the field, that is, the Unruh-Minkowski photon emitted by one atom cannot be absorbed by the other atom.We discuss examples demonstrating interesting features of Minkowski vacuum entanglement.
Quantum effects in accelerated frames and gravitational fields have been studied for decades. One of the most influential outcomes is the discovery of thermal radiation from a black hole by Hawking in 1975. Other important discoveries include the Unruh effect, dynamical Casimir effect etc.. Although these discoveries are very exciting, experimental verification of them is extremely challenging. Even in the theoretical aspect, not all the issues have been resolved, e.g., the well known black hole information paradox. Quantum information science was developed rapidly during the last thirty years. The well established concepts and tools in quantum information science have been used to explore the quantum effects in gravitational fields and relativistic frames, giving birth to a new research field named relativistic quantum information. This thesis studies quantum effects in accelerated frames and gravitational fields by exploiting the concepts and techniques in quantum information science. The Unruh effect implies that the state of the fields confined within part of the Minkowski spacetime can appear thermal, and entanglement exists between different spacetime regions. We show that the particle number distribution of the field modes confined within a finite diamond region is also thermal in the Minkowski vacuum, an analogue to the Unruh effect; and there exists entanglement between different diamonds. The vacuum entanglement can be extracted and utilized for some quantum information protocols, e.g., quantum key distribution. Furthermore, we show that the presence of a horizon and the Unruh thermal noise has important consequences to the quantum communication protocols where one of the parties is a uniformly accelerated observer. Interactions between uniformly accelerated objects and quantum fields are traditionally studied using perturbation theory. The quantum circuit model, a crucial tool in quantum communication and computation, can be exploited to calculate radiations from the uniformly accelerated objects non-perturbatively. By further combining field detection scheme in quantum optics, e.g., homodyne detection, the output field from the uniformly accelerated objects can be fully studied. These techniques help to study decoherence effect in non-inertial frames, which may provide important insights for the black hole information paradox. Dynamical spacetimes generally create quantum particles. Gravitational perturbations around a black hole oscillate and decay, due to the emission of gravitational waves to spatial infinity and into the black hole. We show that they play the role as a multimode squeezer, squeezing the state of the quantum fields and creating particles.
The Hawking effect is an exciting physical prediction lying at the intersection of the two most successful theories of the past century, namely, Einstein’s theory of relativity and quantum mechanics. In this dissertation, we put special emphasis on the quantum aspects of the Hawking process encoded in the entanglement shared by the emitted fluxes of created quanta. In particular, we employ sharp tools from quantum information theory to quantify the entanglement produced by the Hawking effect throughout the black hole evaporation process. Our framework allows us to extend previous calculations of entanglement to a larger set of cases, for instance, the situation where a black hole is immersed in a thermal bath, such as the cosmic microwave background (CMB), and the quantum state of infalling radiation is, therefore, mixed. Motivated by recent intense experimental efforts, we extend our framework to the case of an optical white-black hole pair analog gravity system created by a strong electromagnetic pulse propagating in a non-linear dielectric medium. One of the main results presented in this dissertation is the development of a numerical code that recreates the Hawking process in such an optical analog. Utilizing this code together with our quantum information tools, we study how different input quantum states of light alter the amount of the entanglement produced in the Hawking pairs. We find that although ambient thermal noise and detector inefficiencies, unsurprisingly, tend to reduce quantum correlations in the Hawking process, when horizons are illuminated with single-mode squeezed states of light, the entanglement generated increases in a tunable manner. As a last application in optical analogs, we investigate the laser configuration in which two strong electromagnetic pulses propagate in a non-linear dielectric medium exchanging Hawking quanta, thus, stimulating each other. In such a setup, we observe that not only the number of Hawking quanta created is exponentially increased but also the entanglement shared between the mode of the electromagnetic field inside the laser cavity with the modes of the field outside the cavity grows with time. We conclude that these novel results open a promising window for the observability of the quantum origin of the Hawking effect in the lab.
We review the results obtained by investigating, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups, the time evolution of quantum entanglement of two different bimodal systems, each one interacting with a thermal environment. The first system is formed of the free massless bosonic mode of a stationary observer in a region that is asymptotically flat (Kruskal observer) or freely falling in Schwarzschild black hole, and the mode of a uniformly accelerated observer hovering outside the event horizon of black hole. For initial bimodal Gaussian squeezed thermal states of the system, we show that under the influence of Hawking radiation the quantum entanglement of the two modes is destroyed in a finite time, for non-zero values of the temperature of the thermal environment, i.e. the phenomenon of entanglement sudden death takes place. The second system consists of two bosonic modes associated with a scalar quantum field in de Sitter space, characterized by two regions that are causally disconnected and described using open universe coordinates on two open charts. The survival time of the entanglement of this bimodal system strongly depends on the competition between the contrary effects provided by the squeezing of the initial bimodal state, the curvature of de Sitter space, the mass parameter and the thermal environment. It is shown that the entanglement is minimized for values 1/2 and 3/2 of the mass parameter, corresponding to the conformally coupled scalar field and, respectively, minimally coupled massless field.
The influence of Hawking radiation on quantum entanglement for bimodal Gaussian states near a Schwarzschild black hole is investigated. It is shown that for a thermal squeezed state of a bimodal bosonic system the Hawking radiation reduces and even can destroy the entanglement between the mode of a Kruskal observer Alice and the mode of Bob, who is an accelerated observer hovering outside the event horizon of black hole. By contrary, the Hawking radiation increases and even can generate quantum entanglement between Bob and anti-Bob, who is a hypothetical observer inside event horizon. We show that in both these scenarios the competition between the contrary influences produced by Hawking temperature, squeezing and field frequency, may favour the preservation of the quantum entanglement. We investigate also the influence of the thermal environment on the behaviour in time of the entanglement between the considered observers and show that the entanglement is destroyed in a finite time for both considered bipartite scenarios of observers Alice and Bob, and respectively Bob and anti-Bob, for non-zero values of the temperature of the thermal environment, i.e. the phenomenon of entanglement sudden death takes place. For a zero temperature of the thermal bath the initial existing entanglement is decreasing over time, but it keeps for all finite times a non-zero value and the logarithmic negativity tends to zero only in the limit of infinite time.
The aim of this work is present the phenomenon denoted entanglement harvesting.We begin by introducing entanglement historically.Following, we go beyond the one particle theory in flat spacetime and introduce Quantum Field Theory in Curved Spacetime, showing two famous consequences: the Unruh effect and the Hawking radiation.Finally, we analyze entanglement harvesting for two Unruh-deWitt detectors.In the fisrt example, we see that there is a "sudden death" point of entanglement harvesting when the detectors are near the BTZ black hole event horizon, due to redshift effect and Hawking radiation.Then, we compare the phenomenon for different scenarios, and find out that it is sensitive to the structure of spacetime.Finally, we see how detectors' parameters affect it and find out that the smoothness of the switching of the detectors' coupling to the field is extremely relevant.We also see how the parameters can be used to optimize entanglement harvested.